There are two types of dry yeast: instant yeast, which can be added directly to a dough mixture, and (traditional) active yeast, which must first be mixed with lukewarm water before use.
Store in the Fridge
Once the package is open, keep the yeast in the fridge or store it in the freezer. In either case, make sure that the container is airtight. And rely on the expiry date on the package.
Test the Yeast
How do you ensure that your stored yeast is still active before using it? Mix one teaspoon of it with a little sugar in lukewarm water. The water must be neither too hot nor too cold for the chemical reaction to happen. If bubbles appear and the liquid has doubled after 10 minutes, then the yeast is still good.
To learn more about yeast, read this article: